Predicting Composition-Structure Relations in Alkali Borosilicate Glasses Using Statistical Mechanics

Abstract

Predicting the atomic-scale structure of multicomponent glasses from their composition and thermal history would greatly accelerate the discovery of new engineering and functional glasses. A statistical mechanics-based approach has recently been applied to predict the composition-structure evolution in binary oxide glasses by determining the relative entropic and enthalpic contributions to the bonding preferences. In this work, we first establish the network modifier-former interaction parameters in sodium silicate and sodium borate glasses to predict the structural evolution in sodium borosilicate glasses. Due to the significant variations in the experimentally determined structural speciation in borosilicate glasses, we perform classical molecular dynamics (MD) simulations to establish and validate our structural model. We also show that the statistical mechanical model naturally accounts for the difference in structural speciation from MD simulations and NMR experiments, which in turn arises from the difference in cooling rate and thus thermal history of the glasses. Finally, we demonstrate the predictive capability of the model by accurately accounting for the structural evolution in potassium borosilicate glasses without using any adjustable model parameters. This is possible, because all the interaction parameters are already established in the potassium silicate, potassium borate, and sodium borosilicate glasses, respectively.

Structure Dependence of Poisson’s Ratio in Cesium Silicate and Borate Glasses

“…The structure of the present silicate and borate glasses are predicted using a statistical mechanics model [38] based on existing 29 Si and 11 B magic angle spinning (MAS) NMR spectroscopy data for other compositions [20,39]. The silicate network becomes increasingly depolymerized with increasing cesium content visible by the decrease in Q 4 species (Supplementary Figure S1) and, thus, an increase in Q 3 species.…”

“…Here, the boron and phosphorus containing glasses are new compared to the original study [7]. The number of bridging oxygens is either taken directly from the reference, calculated from NMR data (Q n or B 3/4 units) if available (these describe whether the oxygen bonded to a Si unit or B unit is bonded to another Si/B or is an ionic oxygen charge balanced by modifier ions), predicted from statistical modelling (as described in Figure 1 and Supplementary Figures S1 and S2) [38,65], or estimated as Equation (7),…”

“…Structural assumptions of network forming cations (silicon Q 2 , Q 3 , and Q 4 and boron B 3 and B 4 ) are based on statistical mechanics predictions (see, e.g., Ref. [38]) using NMR data from Dupree et al [22] and Zhong and Bray [39], while cesium is expected to be six-fold coordinated. The ionic radii of cesium, boron, silicon, and oxygen are taken from the work of Shannon [40].…”

Topological model of alkali germanate glasses and exploration of the germanate anomaly

“…2, from the statistical mechanics model 53 for the considered structural transitions. Explicit details of the calculations are extensive and can be found in previous works by Bødker et al 53,65,66 The first transition outlined, Q 4 N 6 , is the → baseline transition which was used for normalization. 19 showing that the increase in N 6 units occurs only until about 20% modifier oxide (x), after which it continuously decreases.…”

“…In order to calculate the H i model parameters based on the relevant structural evolution, a Python script was developed based on a basin-hopping algorithm which determines the global minimum in the error between the fit and the experimental values. Further details can be found in the extensive works of Bødker et al 53,65,66 Due to the difficulty of using NMR spectroscopy to study germanate glasses, the model was not fit to experimental NMR data, but rather fitted to the proposed structural model by Kiczenski et al 19 shown in Figure 1. It is worth noting that this structural model is, in turn, based on the experimental work of Jain et al 40 for the rubidium germanate system.…”